1407edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
Adopt template: Factorization; misc. cleanup |
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== Theory == | == Theory == | ||
1407edo is excellent in the 7-limit, in which it supports the 441 & | 1407edo is excellent in the 7-limit, in which it supports the 441 & 966 [[akjayland]] temperament with period 21. Just like 441edo, it [[tempering out|tempers out]] the [[akjaysma]] and the [[landscape comma]]. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9. | ||
It tunes the [[pure bastille]] temperament in the 1407eff val and the [[marvelous bastille]] temperament in the [[patent val]] in the 13-limit. | It tunes the [[pure bastille]] temperament in the 1407eff val and the [[marvelous bastille]] temperament in the [[patent val]] in the 13-limit. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
1407 | Since 1407 factors into {{factorization|1407}}, 1407edo has subset edos {{EDOs| 3, 7, 21, 67, 201, and 469 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
Revision as of 09:20, 31 October 2023
| ← 1406edo | 1407edo | 1408edo → |
Theory
1407edo is excellent in the 7-limit, in which it supports the 441 & 966 akjayland temperament with period 21. Just like 441edo, it tempers out the akjaysma and the landscape comma. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.
It tunes the pure bastille temperament in the 1407eff val and the marvelous bastille temperament in the patent val in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.036 | +0.040 | +0.044 | -0.358 | +0.411 | -0.051 | +0.142 | +0.297 | -0.153 | +0.380 |
| Relative (%) | +0.0 | -4.2 | +4.7 | +5.2 | -42.0 | +48.1 | -6.0 | +16.6 | +34.8 | -17.9 | +44.6 | |
| Steps (reduced) |
1407 (0) |
2230 (823) |
3267 (453) |
3950 (1136) |
4867 (646) |
5207 (986) |
5751 (123) |
5977 (349) |
6365 (737) |
6835 (1207) |
6971 (1343) | |
Subsets and supersets
Since 1407 factors into 3 × 7 × 67, 1407edo has subset edos 3, 7, 21, 67, 201, and 469.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 814\1407 | 694.243 | [381 0 -159 -4⟩ | Bastille (2.5.7) / pure bastille (1407eff) / marvelous bastille (1407) |
| 3 | 292\1407 | 249.040 | 1536/1331 | Tribilo |
| 7 | 10\1407 | 8.529 | 1029/1024 | Nitrogen |
| 21 | 686\1407 (16\1407) |
585.074 (13.646) |
91875/65536 (126/125) |
Akjayland |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct